SUMS: Gardiner -- The Maths of SET

SUMS (Sydney Uni Maths Society) talks are being held at 1pm each Thursday in New Law 104
this semester.  Free pizza is on offer afterwards! This week’s talk is by Sean
Gardiner.  

Abstract: SET is an award-winning card game invented by geneticist Marsha Falco in
1974.  Each card displays a number of coloured, shaded shapes, and each of these four
attributes can take three different possible values.  A set is then any triple in which
for each attribute, either all three match, or all three differ.  

This talk will demonstrate how the game of SET is really just four-dimensional toroidal
noughts and crosses in disguise, and will answer some of the natural combinatorial
questions that arise along the way.  Particular emphasis will be given to the problem of
determining how many cards must be drawn before a set is guaranteed amongst them, which
is analogous to determining maximal caps in n-dimensional finite fields (which,
surprisingly, is an unsolved problem over F_3 for n>5).